Computational fluid dynamics (CFD) is an important tool for the simulation of the cardiovascular function and dysfunction. Due to the complexity of the anatomy, the transitional regime of blood flow in the heart, and the strong mutual influence between the flow and the physical processes involved in the heart function, the development of accurate and efficient CFD solvers for cardiovascular flows is still a challenging task. In this paper we present lifex-cfd: an open-source CFD solver for cardiovascular simulations based on the lifex finite element library, written in modern C++ and exploiting distributed memory parallelism. We model blood flow in both physiological and pathological conditions via the incompressible Navier-Stokes equations, accounting for moving cardiac valves, moving domains, and transition-to-turbulence regimes. In this paper, we provide an overview of the underlying mathematical formulation, numerical discretization, implementation details and instructions for use of lifex-cfd. The code has been verified through rigorous convergence analyses, and we show its almost ideal parallel speedup. We demonstrate the accuracy and reliability of the numerical methods implemented through a series of idealized and patient-specific vascular and cardiac simulations, in different physiological flow regimes. The lifex-cfd source code is available under the LGPLv3 license, to ensure its accessibility and transparency to the scientific community, and to facilitate collaboration and further developments.
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The In-Network Computing (COIN) paradigm is a promising solution that leverages unused network resources to perform some tasks to meet up with computation-demanding applications, such as metaverse. In this vein, we consider the metaverse partial computation offloading problem for multiple subtasks in a COIN environment to minimise energy consumption and delay while dynamically adjusting the offloading policy based on the changing computation resources status. We prove that the problem is NP and thus transformed it into two subproblems: task splitting problem (TSP) on the user side and task offloading problem (TOP) on the COIN side. We modelled the TSP as an ordinal potential game (OPG) and proposed a decentralised algorithm to obtain its Nash Equilibrium (NE). Then, we model the TOP as Markov Decision Process (MDP) proposed double deep Q-network (DDQN) to solve for the optimal offloading policy. Unlike the conventional DDQN algorithm, where intelligent agents sample offloading decisions randomly within a certain probability, our COIN agent explores the NE of the TSP and the deep neural network. Finally, simulation results show that our proposed model approach allows the COIN agent to update its policies and make more informed decisions, leading to improved performance over time compared to the traditional baseline.
The widespread adoption of edge computing has emerged as a prominent trend for alleviating task processing delays and reducing energy consumption. However, the dynamic nature of network conditions and the varying computation capacities of edge servers (ESs) can introduce disparities between computation loads and available computing resources in edge computing networks, potentially leading to inadequate service quality. To address this challenge, this paper investigates a practical scenario characterized by dynamic task offloading. Initially, we examine traditional Multi-armed Bandit (MAB) algorithms, namely the $\varepsilon$-greedy algorithm and the UCB1-based algorithm. However, both algorithms exhibit certain weaknesses in effectively addressing the tidal data traffic patterns. Consequently, based on MAB, we propose an adaptive task offloading algorithm (ATOA) that overcomes these limitations. By conducting extensive simulations, we demonstrate the superiority of our ATOA solution in reducing task processing latency compared to conventional MAB methods. This substantiates the effectiveness of our approach in enhancing the performance of edge computing networks and improving overall service quality.
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective boundary conditions. The fixed point method to solve the system is shown to be monotone. The discretization is done with a $P^1$ Finite Element Method. The convolution integrals are precomputed at every vertices of the mesh and stored in compressed hierarchical matrices, using Partially Pivoted Adaptive Cross-Approximation. Then the fixed point iterations involve only matrix vector products. The method is $O(N\sqrt[3]{N}\ln N)$, with respect to the number of vertices, when everything is smooth. A numerical implementation is proposed and tested on two examples. As there are some analogies with ray tracing the programming is complex.
Parameter inference for ordinary differential equations (ODEs) is of fundamental importance in many scientific applications. While ODE solutions are typically approximated by deterministic algorithms, new research on probabilistic solvers indicates that they produce more reliable parameter estimates by better accounting for numerical errors. However, many ODE systems are highly sensitive to their parameter values. This produces deep local minima in the likelihood function -- a problem which existing probabilistic solvers have yet to resolve. Here, we show that a Bayesian filtering paradigm for probabilistic ODE solution can dramatically reduce sensitivity to parameters by learning from the noisy ODE observations in a data-adaptive manner. Our method is applicable to ODEs with partially unobserved components and with arbitrary non-Gaussian noise. Several examples demonstrate that it is more accurate than existing probabilistic ODE solvers, and even in some cases than the exact ODE likelihood.
In this paper, we will outline a novel data-driven method for estimating functions in a multivariate nonparametric regression model based on an adaptive knot selection for B-splines. The underlying idea of our approach for selecting knots is to apply the generalized lasso, since the knots of the B-spline basis can be seen as changes in the derivatives of the function to be estimated. This method was then extended to functions depending on several variables by processing each dimension independently, thus reducing the problem to a univariate setting. The regularization parameters were chosen by means of a criterion based on EBIC. The nonparametric estimator was obtained using a multivariate B-spline regression with the corresponding selected knots. Our procedure was validated through numerical experiments by varying the number of observations and the level of noise to investigate its robustness. The influence of observation sampling was also assessed and our method was applied to a chemical system commonly used in geoscience. For each different framework considered in this paper, our approach performed better than state-of-the-art methods. Our completely data-driven method is implemented in the glober R package which is available on the Comprehensive R Archive Network (CRAN).
Federated Machine Learning (FL) has received considerable attention in recent years. FL benchmarks are predominantly explored in either simulated systems or data center environments, neglecting the setups of real-world systems, which are often closely linked to edge computing. We close this research gap by introducing FLEdge, a benchmark targeting FL workloads in edge computing systems. We systematically study hardware heterogeneity, energy efficiency during training, and the effect of various differential privacy levels on training in FL systems. To make this benchmark applicable to real-world scenarios, we evaluate the impact of client dropouts on state-of-the-art FL strategies with failure rates as high as 50%. FLEdge provides new insights, such as that training state-of-the-art FL workloads on older GPU-accelerated embedded devices is up to 3x more energy efficient than on modern server-grade GPUs.
Matrix-variate time series data are largely available in applications. However, no attempt has been made to study their conditional heteroskedasticity that is often observed in economic and financial data. To address this gap, we propose a novel matrix generalized autoregressive conditional heteroskedasticity (GARCH) model to capture the dynamics of conditional row and column covariance matrices of matrix time series. The key innovation of the matrix GARCH model is the use of a univariate GARCH specification for the trace of conditional row or column covariance matrix, which allows for the identification of conditional row and column covariance matrices. Moreover, we introduce a quasi maximum likelihood estimator (QMLE) for model estimation and develop a portmanteau test for model diagnostic checking. Simulation studies are conducted to assess the finite-sample performance of the QMLE and portmanteau test. To handle large dimensional matrix time series, we also propose a matrix factor GARCH model. Finally, we demonstrate the superiority of the matrix GARCH and matrix factor GARCH models over existing multivariate GARCH-type models in volatility forecasting and portfolio allocations using three applications on credit default swap prices, global stock sector indices, and future prices.
Nonparametric estimation of the mean and covariance functions is ubiquitous in functional data analysis and local linear smoothing techniques are most frequently used. Zhang and Wang (2016) explored different types of asymptotic properties of the estimation, which reveal interesting phase transition phenomena based on the relative order of the average sampling frequency per subject $T$ to the number of subjects $n$, partitioning the data into three categories: ``sparse'', ``semi-dense'' and ``ultra-dense''. In an increasingly available high-dimensional scenario, where the number of functional variables $p$ is large in relation to $n$, we revisit this open problem from a non-asymptotic perspective by deriving comprehensive concentration inequalities for the local linear smoothers. Besides being of interest by themselves, our non-asymptotic results lead to elementwise maximum rates of $L_2$ convergence and uniform convergence serving as a fundamentally important tool for further convergence analysis when $p$ grows exponentially with $n$ and possibly $T$. With the presence of extra $\log p$ terms to account for the high-dimensional effect, we then investigate the scaled phase transitions and the corresponding elementwise maximum rates from sparse to semi-dense to ultra-dense functional data in high dimensions. Finally, numerical studies are carried out to confirm our established theoretical properties.
As the saying goes, sometimes less is more -- and when it comes to neural networks, that couldn't be more true. Enter pruning, the art of selectively trimming away unnecessary parts of a network to create a more streamlined, efficient architecture. In this paper, we introduce a novel end-to-end pipeline for model pruning via the frequency domain. This work aims to shed light on the interoperability of intermediate model outputs and their significance beyond the spatial domain. Our method, dubbed Common Frequency Domain Pruning (CFDP) aims to extrapolate common frequency characteristics defined over the feature maps to rank the individual channels of a layer based on their level of importance in learning the representation. By harnessing the power of CFDP, we have achieved state-of-the-art results on CIFAR-10 with GoogLeNet reaching an accuracy of 95.25%, that is, +0.2% from the original model. We also outperform all benchmarks and match the original model's performance on ImageNet, using only 55% of the trainable parameters and 60% of the FLOPs. In addition to notable performances, models produced via CFDP exhibit robustness to a variety of configurations including pruning from untrained neural architectures, and resistance to adversarial attacks. The implementation code can be found at //github.com/Skhaki18/CFDP.
Recommender system is one of the most important information services on today's Internet. Recently, graph neural networks have become the new state-of-the-art approach of recommender systems. In this survey, we conduct a comprehensive review of the literature in graph neural network-based recommender systems. We first introduce the background and the history of the development of both recommender systems and graph neural networks. For recommender systems, in general, there are four aspects for categorizing existing works: stage, scenario, objective, and application. For graph neural networks, the existing methods consist of two categories, spectral models and spatial ones. We then discuss the motivation of applying graph neural networks into recommender systems, mainly consisting of the high-order connectivity, the structural property of data, and the enhanced supervision signal. We then systematically analyze the challenges in graph construction, embedding propagation/aggregation, model optimization, and computation efficiency. Afterward and primarily, we provide a comprehensive overview of a multitude of existing works of graph neural network-based recommender systems, following the taxonomy above. Finally, we raise discussions on the open problems and promising future directions of this area. We summarize the representative papers along with their codes repositories in //github.com/tsinghua-fib-lab/GNN-Recommender-Systems.
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